Heat the oil and butter in a saute pan, and add the celery, carrot, onion, garlic and the bay leaf.
Cook the vegetables over medium heat until the onion is transparent about 20 minutes.
Discard the garlic.
Pat the tripe dry with paper towels and add it to the pan.
Pour the wine into the pan, increase the heat and cook the mixture until the wine has evaporated.
Add the tomatoes and salt and pepper.
Pour in enough stock to cover the tripe.
Cover the pan and simmer for at least two hours, or until the tripe is tender; stir occasionally and add stock, if necessary, to keep the tripe covered.
Add the basil leaves and stir.
Sprinkle the dish with the grated Parmesan cheese before serving.